Transformations of Linear Functions

Front

What is a vertical translation of a function?

Back

A vertical translation moves the graph of a function up or down without changing its shape. For example, replacing f(x) with f(x) + c translates the graph up by c units if c > 0, and down by c units if c < 0.

Front

What happens to the graph of f(x) when it is replaced with f(x) + 2?

Back

The graph of f(x) shifts vertically up by 2 units.

Front

What is a horizontal translation of a function?

Back

A horizontal translation moves the graph of a function left or right. For example, replacing f(x) with f(x - c) shifts the graph right by c units if c > 0, and left by c units if c < 0.

Front

What happens to the graph of f(x) when it is replaced with f(x - 4)?

Back

The graph of f(x) shifts horizontally right by 4 units.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1. For example, replacing f(x) with kf(x) where k > 1 stretches the graph vertically.

Front

What happens to the graph of f(x) when it is replaced with 2f(x)?

Back

The graph of f(x) undergoes a vertical stretch by a factor of 2.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1. For example, replacing f(x) with kf(x) where 0 < k < 1 compresses the graph vertically.

Front

What is a reflection across the x-axis?

Back

A reflection across the x-axis occurs when the output of a function is multiplied by -1. For example, replacing f(x) with -f(x) flips the graph over the x-axis.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which is a straight line passing through the origin with a slope of 1.

Front

How does the graph of g(x) = f(x) + 3 compare to f(x)?

Back

The graph of g(x) is the same as f(x) but shifted vertically up by 3 units.